Exploring Welfare Maximization and Fairness in Participatory Budgeting

Abstract

Participatory budgeting (PB) is a voting paradigm for distributing a divisible resource, usually called a budget, among a set of projects by aggregating the preferences of individuals over these projects. It is implemented quite extensively for purposes such as government allocating funds to public projects and funding agencies selecting research proposals to support. This dissertation studies the welfare-related and fairness-related objectives for different PB models. Our contribution lies in proposing and exploring novel PB rules that maximize welfare and promote fairness, as well as, in introducing and investigating a range of novel utility notions, axiomatic properties, and fairness notions, effectively filling the gaps in the existing literature for each PB model. The thesis is divided into two main parts, the first focusing on dichotomous and the second focusing on ordinal preferences. Each part considers two cases: (i) the cost of each project is restricted to a single value and partial funding is not permitted and (ii) the cost of each project is flexible and may assume multiple values.

For each of the four PB models, we propose novel PB rules that maximize welfare or promote fairness. To maximize welfare, we study utility notions existing in the literature and also introduce new notions tailored to each model. We propose PB rules that optimize utilitarian or egalitarian welfare and thoroughly analyze the computational and axiomatic aspects of these rules. In the context of fairness, we critically assess existing notions, emphasizing their limitations and drawbacks. We put forward novel fairness notions which overcome these limitations, and either construct or characterize several families of innovative fair PB rules. Furthermore, we investigate the computational complexity of the newly proposed fair PB rules.